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Summary form only given. The gamma-ray laser dilemma states that incoherent pump required to produce a population inversion would unavoidable destroy the conditions of the Mossbauer and Borrmann effects which are crucial for realization of the net gain. For four decades this dilemma prevailed all over the researches on gamma-ray lasers, making hopeless any attempt to approach a problem of gamma-ray laser. Recently it was shown that laser driving of bounded electronic transitions in atoms provides efficient manipulation by the Mossbauer spectra of nuclear transitions. Under certain conditions it leads to suppression of resonant absorption by 3-5 orders of magnitude reducing it up to the level of off-resonant losses in the host matrix. In turn, suppression of the resonant absorption reduces by the same amount the requirement for incoherent pump and accordingly heating of the active sample. This allows to pump active nuclei in the host lattice without destroying the conditions of both Mossbauer and Borrmann effects. Moreover it allows to pump resonantly at the operating transition that increases additionally the efficiency of the incoherent pump by 1-2 orders of magnitude. All together gamma-ray laser schemes involving laser driving of electronic transitions reduce the laser threshold by 4-7 orders of magnitude and hence suggest a completely new path for solution of the gamma-ray laser problem.